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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Anosov flows and expansiveness


Authors: Victor Norton and Thomas O’Brien
Journal: Proc. Amer. Math. Soc. 40 (1973), 625-628
MSC: Primary 58F15
DOI: https://doi.org/10.1090/S0002-9939-1973-0322907-X
MathSciNet review: 0322907
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Abstract: We prove that an Anosov diffeomorphism of a compact manifold is expansive. We also show that a continuous flow on an infinite compact metric space cannot be expansive. We define a corresponding expansive concept for flows, that of an unstable flow (the word unstable is used here in a Lyapunov sense). We then prove that Anosov flows of compact manifolds are unstable.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0322907-X
Keywords: Anosov diffeomorphism, Anosov flow, expansive, unstable
Article copyright: © Copyright 1973 American Mathematical Society